簡約 ((-1)/2)^{(-1)/2}

解

簡約

(\frac{- 1}{2})^{\frac{- 1}{2}}

- 2^{\frac{1}{2}} i

解答ステップ

(\frac{- 1}{2})^{\frac{- 1}{2}}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - 1 ) ^{\frac{- 1}{2}}}{2 ^{\frac{- 1}{2}}}

(- 1)^{\frac{- 1}{2}} = \frac{1}{i}

= \frac{\frac{1}{i}}{2 ^{\frac{- 1}{2}}}

2^{\frac{- 1}{2}} = \frac{1}{2 ^{\frac{1}{2}}}

= \frac{\frac{1}{i}}{\frac{1}{2 ^{\frac{1}{2}}}}

簡素化

\frac{\frac{1}{i}}{\frac{1}{2 ^{\frac{1}{2}}}} : \frac{2 ^{\frac{1}{2}}}{i}

= \frac{2 ^{\frac{1}{2}}}{i}

共役で乗じる

\frac{- i}{- i}

= \frac{2 ^{\frac{1}{2}} ( - i )}{i ( - i )}

簡素化

\frac{2 ^{\frac{1}{2}} ( - i )}{i ( - i )} : \frac{- 2 ^{\frac{1}{2}} i}{1}

= \frac{- 2 ^{\frac{1}{2}} i}{1}

分数の規則を適用する:

\frac{a}{1} = a

= - 2^{\frac{1}{2}} i